# LRD spectral analysis of multifractional functional time series on manifolds

arXiv: https://arxiv.org/abs/2212.06228 · HTML: https://mlsanity.com/paper/2212.06228/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Time-adaptive infinite-dimensional Gaussian process regression on manifolds](https://mlsanity.com/paper/2603.21144/) (2026)

## Abstract (arXiv)

This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert-Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved under a semiparametric functional spectral framework in the Gaussian context. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The performance of both estimation procedures is illustrated in the simulation study, in the context of multifractionally integrated spherical functional autoregressive-moving average (SPHARMA(p,q)) processes.